Optimization of thin film growth using multiscale process systems

In this work we consider optimization problems for transport-reaction processes, when the cost function and/or equality constraints necessitate the consideration of phenomena that occur over widely disparate length scales. Initially, we develop multiscale process models that link continuum conservation laws with microscopic scale simulators. Subsequently, we combine nonlinear order reduction techniques for dissipative partial-differential equation systems with adaptive tabulation methods for microscopic simulators to reduce the computational requirements of the process description. The optimization problem is subsequently solved using standard search algorithms. The proposed method is applied to a representative thin film deposition process, where we compute optimal surface temperature profiles that simultaneously maximize deposition-rate uniformity (macroscale objective) and minimize surface roughness (microscale objective) across the film surface.

[1]  Lorenz T. Biegler,et al.  Reduced successive quadratic programming implementation for large-scale optimization problems with smaller degrees of freedom , 1990 .

[2]  P. Coveney,et al.  Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Christodoulos A. Floudas,et al.  Global Optimization with Nonfactorable Constraints , 2002 .

[4]  W. H. Weinberg,et al.  Theoretical foundations of dynamical Monte Carlo simulations , 1991 .

[5]  K. Jensen,et al.  MULTISCALE MODELING OF THIN FILM GROWTH , 1998 .

[6]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[7]  P. Christofides,et al.  Dynamic optimization of dissipative PDE systems using nonlinear order reduction , 2002 .

[8]  Martha A. Gallivan.  Optimization, estimation, and control for kinetic Monte Carlo simulations of thin film deposition , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[9]  P. Christofides,et al.  Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes , 2002 .

[10]  Richard E. Mortensen,et al.  Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam) , 1991, SIAM Rev..

[11]  Michael Tsapatsis,et al.  Multiscale hybrid modeling of film deposition within porous substrates , 2004 .

[12]  J. Q. Broughton,et al.  Concurrent coupling of length scales: Methodology and application , 1999 .

[13]  C. Kelley,et al.  Truncated Newton Methods for Optimization with Inaccurate Functions and Gradients , 2003 .

[14]  Dionisios G. Vlachos,et al.  Low-Dimensional Approximations of Multiscale Epitaxial Growth Models for Microstructure Control of Materials , 2000 .

[15]  D. Vlachos.  Multiscale integration hybrid algorithms for homogeneous–heterogeneous reactors , 1997 .

[16]  Alejandro L. Garcia,et al.  Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo , 1999 .

[17]  Eirik Grude Flekkøy,et al.  Hybrid model for combined particle and continuum dynamics , 2000 .

[18]  Sidney Yip,et al.  Nearly exact solution for coupled continuum/MD fluid simulation , 1999 .

[19]  O'Connell,et al.  Molecular dynamics-continuum hybrid computations: A tool for studying complex fluid flows. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  P. Christofides,et al.  Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models , 2003 .

[21]  A. Armaou,et al.  Dynamic optimization of dissipative PDEs using control vector parameterization: application to GaN thin film epitaxy , 2004, Proceedings of the 2004 American Control Conference.

[22]  Panagiotis D. Christofides,et al.  Optimization of transport-reaction processes using nonlinear model reduction , 2000 .

[23]  Constantinos Theodoropoulos,et al.  Equation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks , 2002 .

[24]  A. Armaou,et al.  Multiscale optimization using hybrid PDE/kMC process systems with application to thin film growth , 2005 .

[25]  P. Christofides,et al.  Feedback control of growth rate and surface roughness in thin film growth , 2003 .

[26]  P. Christofides,et al.  A computationally efficient method for optimization of transport-reaction processes , 1999 .

[27]  N. Hadjiconstantinou.  Regular Article: Hybrid Atomistic–Continuum Formulations and the Moving Contact-Line Problem , 1999 .

[28]  Stephen B. Pope,et al.  Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation , 1997 .